Related papers: A small collection of open problems
This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…
This paper contains a selection, dictated by personal taste and by no means complete, of open problems in local discrete holomorphic dynamics.
This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of…
A collection of open problems in Costas arrays is presented, classified into several categories, along with the context in which they arise.
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…
The recent interest in Big Data has generated a broad range of new academic, corporate, and policy practices along with an evolving debate amongst its proponents, detractors, and skeptics. While the practices draw on a common set of tools,…
Thousands of complex natural language questions are submitted to community question answering websites on a daily basis, rendering them as one of the most important information sources these days. However, oftentimes submitted questions are…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
Online(-only) friendships have become increasingly common in daily lives post-COVID despite debates around their mental health benefits and equivalence to ''real'' relationships. Previous research has reflected a need to understand how…
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
The dark matter problem is almost a century old. Since the 1930s evidence has been growing that our cosmos is dominated by a new form of non-baryonic matter, that holds galaxies and clusters together and influences cosmic structures up to…
We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections,…
An assessment of the present status of the theory, some immediate tasks which are suggested thereby and some questions whose answers may require a longer breath since they relate to significant changes in the conceptual and mathematical…
This brief article presents the introduction and draft of the fundamental ideas developed at length in the book of the same title, which gives a challenging point of view about science and its history/philosophy/sociology. Science is in…
Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is…
The emergence and popularization of online social networks suddenly made available a large amount of data from social organization, interaction and human behavior. All this information opens new perspectives and challenges to the study of…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our…